UNITED STATES
               SECURITIES AND EXCHANGE COMMISSION
                     Washington, D.C. 20549

                           FORM 10-Q

[X]   Quarterly report pursuant to Section 13 or 15  (d)  of  the
Securities Exchange Act of 1934
For the period ended March 31, 1998 or

[  ]   Transition report pursuant to Section 13 or 15 (d) of  the
Securities Exchange Act of 1934
For the transition period from ________________to_____________

Commission File Number 0-13299

                DEAN WITTER CORNERSTONE FUND III
    (Exact name of registrant as specified in its charter)


                New   York                             13-3190919
(State or other jurisdiction of              (I.R.S. Employer
incorporation or organization)               Identification No.)


c/o Demeter Management Corporation
Two  World  Trade  Center, 62 FL. New  York,  NY            10048
(Address of principal executive offices)           (Zip Code)


Registrant's telephone number, including area code (212) 392-5454

(Former  name, former address, and former fiscal year, if changed
since last report)


Indicate  by check mark whether the registrant (1) has filed  all
reports  required  to be filed by Section  13  or  15(d)  of  the
Securities  Exchange Act of 1934 during the preceding  12  months
(or  for such shorter period that the registrant was required  to
file  such  reports),  and (2) has been subject  to  such  filing
requirements for the past 90 days.

Yes    X       No

                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
<PAGE>
<TABLE>
                                
                DEAN WITTER CORNERSTONE FUND III

             INDEX TO QUARTERLY REPORT ON FORM 10-Q

                         March 31, 1998
<CAPTION>

PART I. FINANCIAL INFORMATION
<S>                                                         <C>
Item 1. Financial Statements

   Statements of Financial Condition
   March 31, 1998 (Unaudited) and December 31, 1997...........2

   Statements of Operations for the Quarters Ended
   March 31, 1998 and 1997 (Unaudited)........................3

   Statements of Changes in Partners' Capital for the
   Quarters Ended March 31, 1998 and 1997 (Unaudited).........4

   Statements of Cash Flows for the Quarters Ended
   March 31, 1998 and 1997 (Unaudited)........................5

   Notes to Financial Statements (Unaudited)...............6-11

Item 2.  Management's Discussion and Analysis of Financial

Condition and Results of Operations..............12-15


PART II. OTHER INFORMATION

Item 1. Legal Proceedings.................................16-17

Item 2. Changes in Securities and Use of Proceeds.........17-19

Item 6. Exhibits and Reports on Form 8-K.....................20





</TABLE>












<PAGE>
<TABLE>

                 PART I.  FINANCIAL INFORMATION
                  ITEM 1.  FINANCIAL STATEMENTS

                DEAN WITTER CORNERSTONE FUND III
               STATEMENTS OF FINANCIAL CONDITION

<CAPTION>

                                     March 31,     December 31,
                                        1998           1997
                                         $              $
                                    (Unaudited)
ASSETS
<S>                              <C>               <C>
Equity in Commodity futures trading accounts:
 Cash                             41,376,875     39,762,715
 Net unrealized gain on open contracts1,631,286   1,938,295
 Net option premiums                  (27,500)      (158,765)

 Total Trading Equity             42,980,661     41,542,245

 Interest receivable (DWR)           143,794        145,100
 Due from DWR                         49,908         94,981

 Total Assets                     43,174,363      41,782,326

LIABILITIES AND PARTNERS' CAPITAL

Liabilities

 Redemptions payable                 212,145         429,759
 Accrued management fees             143,060          138,480
 Common administrative expenses payable   113,255       99,713

 Total Liabilities                   468,460          667,952


Partners' Capital

 Limited Partners (13,091.056 and
  13,352.334 Units, respectively) 41,494,750       39,970,539
 General Partner (382.103 Units)   1,211,153        1,143,835

 Total Partners' Capital          42,705,903       41,114,374

 Total Liabilities and Partners' Capital  43,174,363  41,782,326


NET ASSET VALUE PER UNIT            3,169.70        2,993.52

<FN>
        The accompanying footnotes are an integral part
                 of these financial statements.
</TABLE>
<PAGE>
<TABLE>

                DEAN WITTER CORNERSTONE FUND III
                    STATEMENTS OF OPERATIONS
                           (Unaudited)


<CAPTION>



                                For the Quarters Ended March 31,

                                       1998            1997
                                        $            $
REVENUES
<S>                         <C>              <C>
 Trading profit (loss):
    Realized                      3,312,479      4,228,547
    Net change in unrealized        (307,009)      (5,500)

      Total Trading Results       3,005,470      4,223,047

    Interest Income (DWR)           430,094        453,531

      Total Revenues              3,435,564      4,676,578


EXPENSES

    Brokerage commissions (DWR)     556,591        586,097
    Management fees                 418,738        444,564
    Transaction fees and costs       56,265         59,614
    Common administrative expenses       13,542       19,322

      Total Expenses                1,045,136    1,109,597

NET INCOME                          2,390,428    3,566,981


NET INCOME ALLOCATION:
    Limited Partners                2,323,110    3,478,583
    General Partner                    67,318       88,398


NET INCOME PER UNIT:
    Limited Partners                   176.18       231.35
    General Partner                    176.18       231.35


<FN>

        The accompanying footnotes are an integral part
                 of these financial statements.

</TABLE>
<PAGE>
<TABLE>

                DEAN WITTER CORNERSTONE FUND III
           STATEMENTS OF CHANGES IN PARTNERS' CAPITAL
         For the Quarters Ended March 31, 1998 and 1997
                          (Unaudited)


<CAPTION>

                          Units of
                        Partnership Limited   General
                          Interest   Partners Partner    Total


<S>                          <C>             <C>              <C>
<C>
Partners' Capital
  December 31, 1996     15,479.706 $40,997,752 $1,037,606 $42,035
,358

Offering of Units           1.841     5,000    -         5,000

Net Income                  -     3,478,583    88,398  3,566,981

Redemptions                 (689.609)   (2,017,565)             -
(2,017,565)

Partners' Capital
  March 31, 1997        14,791.938 $42,463,770 $1,126,004 $43,589
,774




Partners' Capital
   December 31, 1997     13,734.437$39,970,539  $1,143,835$41,114
,374

Net Income                -       2,323,110     67,3182,390,428

Redemptions               (261.278)      (798,899)              -
(798,899)

Partners' Capital
    March 31, 1998     13,473.159   $41,494,750    $1,211,153 $42
,705,903



<FN>




         The accompanying footnotes are an integral part
                 of these financial statements.

</TABLE>




<PAGE>
<TABLE>

                DEAN WITTER CORNERSTONE FUND III
                    STATEMENTS OF CASH FLOWS
                           (Unaudited)



<CAPTION>


                                For the Quarters Ended March 31,

                                       1998            1997
                                        $            $
CASH FLOWS FROM OPERATING ACTIVITIES
<S>                         <C>              <C>
 Net income                       2,390,428    3,566,981
 Noncash item included in net income:
    Net change in unrealized        307,009        5,500

 (Increase) decrease in operating assets:
    Net option premiums             (131,265)     27,908
    Interest receivable (DWR)         1,306       (17,391)
    Due from DWR                     45,073       (26,232)

 Increase (decrease) in operating liabilities:
    Accrued management fees           4,580        5,323
    Common administrative expenses payable13,542  19,323
    Accrued brokerage commissions (DWR)-          11,049
       Accrued   transaction   fees   and    costs              -
(3,094)

 Net cash provided by operating activities   2,630,673  3,589,367


CASH FLOWS FROM FINANCING ACTIVITIES

 Offering of units                    -            5,000
 Increase (decrease) in redemptions payable(217,614)42,552
 Redemptions of units               (798,899)  (2,017,565)

 Net cash used for financing activities (1,016,513)(1,970,013)


 Net increase in cash             1,614,160    1,619,354

 Balance at beginning of period  39,762,715    40,587,011

 Balance at end of period        41,376,875     42,206,365


<FN>

        The accompanying footnotes are an integral part
                 of these financial statements.
</TABLE>
<PAGE>
                DEAN WITTER CORNERSTONE FUND III

                  NOTES TO FINANCIAL STATEMENTS

                           (Unaudited)

The  financial statements include, in the opinion of  management,

all  adjustments necessary for a fair presentation of the results

of  operations and financial condition of Dean Witter Cornerstone

Fund  III  (the  "Partnership").  The  financial  statements  and

condensed  notes  herein should be read in conjunction  with  the

Partnership's December 31, 1997 Annual Report on Form 10-K.



1. Organization

Dean  Witter  Cornerstone  Fund  III  is  a  limited  partnership

organized  to  engage  in  the  speculative  trading  of  futures

contracts,   options  contracts,  and  forward  contracts.    The

Partnership  is  one  of  the  Dean  Witter  Cornerstone   Funds,

comprised  of  Dean  Witter  Cornerstone  Fund  II,  Dean  Witter

Cornerstone Fund III, and Dean Witter Cornerstone Fund  IV.   The

general   partner  for  the  Partnership  is  Demeter  Management

Corporation  ("Demeter").  The non-clearing commodity  broker  is

Dean  Witter Reynolds Inc. ("DWR"), with an unaffiliated  broker,

Carr  Futures,  Inc. ("Carr"), providing clearing  and  execution

services.  Both Demeter and DWR are wholly-owned subsidiaries  of

Morgan  Stanley Dean Witter & Co. ("MSDW").  The trading advisors

who  make  all trading decisions for the Partnership are  Abraham

Trading  Co., Welton Investment Systems Corporation  and  Sunrise

Capital Management.







<PAGE>

                DEAN WITTER CORNERSTONE FUND III
           NOTES TO FINANCIAL STATEMENTS (CONTINUED)



2. Related Party Transactions

The  Partnership's  cash  is on deposit  with  DWR  and  Carr  in

commodity trading accounts to meet margin requirements as needed.

DWR  pays  interest on these funds based on current 13-week  U.S.

Treasury   Bill  rates.  Brokerage  expenses  incurred   by   the

Partnership are paid to DWR.



3. Financial Instruments

The Partnership trades futures, options, and forward contracts in

interest   rates,  stock  indices,  commodities  and  currencies.

Futures and forwards represent contracts for delayed delivery  of

an  instrument at a specified date and price.  Risk  arises  from

changes  in  the  value  of  these contracts  and  the  potential

inability  of  counterparties to perform under the terms  of  the

contracts.   There  are numerous factors which may  significantly

influence the market value of these contracts, including interest

rate  volatility.  At March 31, 1998 and December 31, 1997,  open

contracts were:


                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
<PAGE>         DEAN WITTER CORNERSTONE FUND III
           NOTES TO FINANCIAL STATEMENTS (CONTINUED)

                               Contract or Notional Amount
                            March 31, 1998   December 31, 1997
                                    $                   $
Exchange-Traded Contracts
 Financial Futures:
   Commitments to Purchase     30,969,000        50,242,000
   Commitments to Sell         14,399,000        21,172,000
   Options Written              4,173,000              -
 Commodity Futures:
   Commitments to Purchase      8,216,000         8,055,000
   Commitments to Sell         20,638,000        31,622,000
   Options Written                485,000               -
 Foreign Futures:
   Commitments to Purchase     60,626,000        50,870,000
   Commitments to Sell         20,033,000        42,064,000
Off-Exchange-Traded
 Forward Currency Contracts
   Commitments to Purchase     13,473,000        27,863,000
   Commitments to Sell         29,648,000         41,794,000


A  portion of the amounts indicated as off-balance-sheet risk  in

forward   currency   contracts  is  due  to  offsetting   forward

commitments  to purchase and sell the same currency on  the  same

date   in   the   future.   These  commitments  are  economically

offsetting,  but are not offset in the forward market  until  the

settlement date.



The  net  unrealized  gain on open contracts  is  reported  as  a

component  of  "Equity in Commodity futures trading accounts"  on

the  Statements of Financial Condition and totaled $1,631,286 and

$1,938,295 at March 31, 1998 and December 31, 1997, respectively.



Of  the $1,631,286 net unrealized gain on open contracts at March

31, 1998, $1,171,945 related to exchange-traded futures contracts



                                

<PAGE>
                                
                DEAN WITTER CORNERSTONE FUND III
            NOTES TO FINANCIAL STATEMENTS (CONTINUED)




and  $459,341  related  to off-exchange traded  forward  currency

contracts.



Of  the  $1,938,295  net unrealized gain  on  open  contracts  at

December 31, 1997, $2,168,497 related to exchange-traded  futures

contracts  and $(230,202) related to off-exchange-traded  forward

currency contracts.



Exchange-traded  futures contracts held  by  the  Partnership  at

March 31, 1998 and December 31, 1997 mature through October  1998

and   June   1998,  respectively.   Off-exchange-traded   forward

currency contracts held by the Partnership at March 31, 1998  and

December  31,  1997  mature through June  1998  and  March  1998,

respectively.



The   contract   amounts  in  the  above  table   represent   the

Partnership's  extent of involvement in the particular  class  of

financial  instrument, but not the credit  risk  associated  with

counterparty  nonperformance.  The credit  risk  associated  with

these  instruments  is limited to the amounts  reflected  in  the

Partnership's Statements of Financial Condition.



The  Partnership also has credit risk because either DWR or  Carr

acts as the futures commission merchant or the counterparty, with

respect  to  most  of  the Partnership's assets.  Exchange-traded

futures and option contracts are marked to market on a daily

<PAGE>

                DEAN WITTER CORNERSTONE FUND III
            NOTES TO FINANCIAL STATEMENTS (CONTINUED)




basis,  with variations in value settled on a daily  basis.   DWR

and  Carr,  as the futures commission merchants for  all  of  the

Partnership's exchange-traded futures and options contracts,  are

required pursuant to regulations of the Commodity Futures Trading

Commission  ("CFTC") to segregate from their own assets  and  for

the sole benefit of their commodity customers, all funds held  by

them with respect to exchange-traded futures and option contracts

including an amount equal to the net unrealized gain on all  open

futures and option contracts, which funds totaled $42,548,820 and

$41,931,212 at March 31, 1998 and December 31, 1997 respectively.

With  respect  to  the Partnership's off-exchange-traded  forward

currency  contracts, there are no daily settlements of variations

in value nor is there any requirement that an amount equal to the

net  unrealized  gain  on open forward contracts  be  segregated.

With   respect  to  those  off-exchange-traded  forward  currency

contracts, the Partnership is at risk to the ability of Carr, the

counterparty  on  all  of  such contracts,  to  perform.   Carr's

parent,   Credit   Agricole  Indosuez,  has   guaranteed   Carr's

obligations to the Partnership.



For  the  quarter  ended March 31, 1998 and for  the  year  ended

December   31,   1997,  the  average  fair  value  of   financial

instruments held for trading purposes was as follows:



                                
<PAGE>
                DEAN WITTER CORNERSTONE FUND III
            NOTES TO FINANCIAL STATEMENTS (CONCLUDED)




                                           March 31, 1998
                                       Assets        Liabilities
                                         $                $
Exchange-Traded Contracts:
  Financial Futures                  57,390,000       14,454,000
  Options on Financial Futures            -           23,616,000
  Commodity Futures                   6,208,000       26,352,000
  Options on Commodity Futures            -              121,000
  Foreign Futures                    82,733,000       26,404,000
Off-Exchange-Traded Forward
 Currency Contracts                  35,752,000       45,639,000

                                
                                
                                
                                          December 31, 1997
                                       Assets        Liabilities
                                         $                $
Exchange-Traded Contracts:
  Financial Futures                  82,881,000       46,462,000
  Options on Financial Futures          698,000       64,639,000
  Commodity Futures                  26,095,000       21,377,000
  Options on Commodity Futures        1,117,000        4,712,000
  Foreign Futures                    44,764,000       26,219,000
  Options on Foreign Futures          7,229,000                -
Off-Exchange-Traded Forward
 Currency Contracts                  12,599,000       13,558,000





















<PAGE>

Item   2.MANAGEMENT'S  DISCUSSION  AND  ANALYSIS   OF   FINANCIAL
CONDITION         AND RESULTS OF OPERATIONS.


Liquidity.  The  Partnership's  assets  on  deposit  in  separate

commodity  trading  accounts with DWR  and  Carr,  the  commodity

brokers,  and are used by the Partnership as margin to engage  in

commodity  futures  contract trading.  DWR  and  Carr  hold  such

assets   in  either  designated  depositories  or  in  securities

approved  by  the  CFTC for investment of  customer  funds.   The

Partnership's assets held by DWR and Carr may be used  as  margin

solely  for  the Partnership's trading.  Since the  Partnership's

sole purpose is to trade in commodity futures contracts and other

commodity  interests,  it is expected that the  Partnership  will

continue to own such liquid assets for margin purposes.



The  Partnership's investment in commodity futures contracts  and

other  commodity interests may be illiquid.  If the price  for  a

futures  contract  for a particular commodity  has  increased  or

decreased  by an amount equal to the "daily limit", positions  in

the  commodity can neither be taken nor liquidated unless traders

are  willing to effect trades at or within the limit.   Commodity

futures  prices  have  occasionally moved  the  daily  limit  for

several consecutive days with little or no trading.  Such  market

conditions   could   prevent   the  Partnership   from   promptly

liquidating its commodity futures positions.

                                

There  is  no limitation on daily price moves in trading  forward

contracts  on  foreign  currency.  The  markets  for  some  world

currencies have low trading volume and are illiquid which may

<PAGE>

prevent  the  Partnership from trading in potentially  profitable

markets  or  prevent  the Partnership from  promptly  liquidating

unfavorable  positions  in  such markets  and  subjecting  it  to

substantial  losses.  Either  of these  market  conditions  could

result in restrictions on redemptions.

                                

Capital  Resources.  The Partnership does not have, nor  does  it

expect to have, any capital assets.  Redemptions and exchanges of

Units  of Limited Partnership Interest in the future will  affect

the  amount  of  funds  available for investments  in  subsequent

periods.   As  redemptions  are  at  the  discretion  of  Limited

Partners,  it  is  not  possible  to  estimate  the  amount   and

therefore, the impact of future redemptions.

                                

Results of Operations

For the Quarter Ended March 31, 1998

For  the  quarter  ended March 31, 1998, the Partnership's  total

trading  revenues  including  interest  income  were  $3,435,564.

During the first quarter, the Partnership recorded a gain in  Net

Asset  Value per Unit.  The most significant gains were  recorded

from  long  U.S.  and European stock index futures  positions  as

prices  in  these markets trended consistently higher  throughout

the quarter.  Additional profits were recorded from long European

bond  futures  positions as prices in these markets also  trended

higher during the quarter.  In energies, gains were recorded from

short  crude oil futures positions as oil prices declined  during

January  and  February  as tensions eased  in  the  Middle  East.

Smaller  gains  were recorded from short positions  in  livestock

futures as prices

<PAGE>

in  these markets moved lower during February.  These gains  were

partially offset by losses experienced in metals from long silver

futures  positions as silver prices reversed lower  during  March

after  trending steadily higher during January and  February  and

from  short gold futures positions as gold prices reversed higher

during  January.  Smaller losses were recorded in  currencies  as

the  value  of  the  Australian dollar and  British  pound  moved

without  consistent  direction  throughout  a  majority  of   the

quarter.    Total  expenses  for  the  period  were   $1,045,136,

resulting  in  net  income  of  $2,390,428.   The  value  of   an

individual  Unit in the Partnership increased from  $2,993.52  at

December 31, 1997 to $3,169.70 at March 31, 1998.



For the Quarter Ended March 31, 1997

For  the  quarter  ended March 31, 1997, the Partnership's  total

trading  revenues  including  interest  income  were  $4,676,578.

During  the first quarter, the Partnership posted an increase  in

Net  Asset  Value  per  Unit.  The most  significant  gains  were

recorded  due  to a strong upward trend in coffee  prices  during

January  and February.  In the agricultural markets,  gains  were

recorded  during  February and March from long soybean  and  corn

futures  positions,  as  prices in  these  markets  also  trended

higher.  Additional  gains  were  recorded  during  January   and

February in the currency markets as the value of the U.S.  dollar

strengthened relative to most major European currencies, as  well

as  the  Japanese yen.  A portion of these gains  was  offset  by

losses recorded from transactions involving the British pound, as

well  as  the  Canadian and Australian dollars.  During  January,

gains were

<PAGE>

recorded  from  long base metals futures positions  as  zinc  and

copper prices moved higher.  A portion of the Partnership's gains

during  the  quarter was offset by losses recorded in the  energy

markets  during  January and March as gas and  oil  prices  moved

without consistent direction.  Smaller losses were experienced in

the financial futures markets as gains recorded during January in

global  stock  index futures were offset by losses recorded  from

choppy  price  movement in global interest  rate  futures  during

February   and  March.  Total  expenses  for  the   period   were

$1,109,597, generating net income of $3,566,981.  The value of an

individual  Unit in the Partnership increased from  $2,715.51  at

December 31, 1996 to $2,946.86 at March 31, 1997.

































<PAGE>

                   PART II.  OTHER INFORMATION

                                

Item 1.   LEGAL PROCEEDINGS

On  September 6, 10, and 20, 1996, and on March 13, 1997, similar

purported class actions were filed in the Superior Court  of  the

State  of  California, County of Los Angeles, on  behalf  of  all

purchasers  of  interest in limited partnership  commodity  pools

sold  by DWR.  Named defendants include DWR, Demeter, Dean Witter

Futures  &  Currency Management Inc. ("DWFCM"),  MSDW  (all  such

parties referred to hereafter as the "Dean Witter Parties"),  the

Partnership, certain other limited partnership commodity pools of

which  Demeter  is  the  general  partner,  and  certain  trading

advisors to those pools.  On June 16, 1997, the plaintiffs in the

above  actions filed a consolidated amended complaint,  alleging,

among  other things, that the defendants committed fraud, deceit,

negligent misrepresentation, various violations of the California

Corporations Code, intentional and negligent breach of  fiduciary

duty,   fraudulent   and   unfair  business   practices,   unjust

enrichment,  and  conversion in the sale  and  operation  of  the

various  limited  partnership commodity pools. Similar  purported

class  actions were also filed on September 18 and 20,  1996,  in

the  Supreme Court of the State of New York, New York County, and

on  November  14,  1996 in the Superior Court  of  the  State  of

Delaware, New Castle County, against the Dean Witter Parties  and

certain trading advisors on behalf of all purchasers of interests

in  various  limited partnership commodity pools,  including  the

Partnership, sold by DWR. A consolidated and amended complaint in

                                

<PAGE>

the  action pending in the Supreme Court of the State of New York

was  filed  on  August  13, 1997, alleging  that  the  defendants

committed   fraud,  breach  of  fiduciary  duty,  and   negligent

misrepresentation  in  the  sale and  operation  of  the  various

limited partnership commodity pools.  On December 16, 1997,  upon

motion  of  the  plaintiffs, the action pending in  the  Superior

Court  of the State of Delaware was voluntarily dismissed without

prejudice.   The   complaints   seek   unspecified   amounts   of

compensatory  and  punitive  damages  and  other  relief.  It  is

possible  that additional similar actions may be filed and  that,

in  the course of these actions, other parties could be added  as

defendants.  The Dean Witter Parties believe that  they  and  the

Partnership  have  strong defenses to, and they  will  vigorously

contest,  the  actions.  Although the ultimate outcome  of  legal

proceedings cannot be predicted with certainty, it is the opinion

of  management of the Dean Witter Parties that the resolution  of

the  actions  will  not  have a material adverse  effect  on  the

financial  condition or the results of operations of any  of  the

Dean Witter Parties or the Partnership.



Item 2.  CHANGES IN SECURITIES AND USE OF PROCEEDS

Dean  Witter  Cornerstone  Fund I ("Cornerstone  I");  Dean  Witter

Cornerstone Fund II ("Cornerstone II"), and Dean Witter Cornerstone

III  ("Cornerstone III") collectively registered 250,000  Units  of

Limited  Partnership Interest ("Units") pursuant to a  Registration

Statement on Form S-1, which became effective on May 31, 1984  (the

"Registration  Statement")  (SEC File  Numbers  2-88587;  88587-01;

88587-02). As contemplated in the Registration Statement, an

<PAGE>

additional fund, Dean Witter Cornerstone Fund IV ("Cornerstone  IV"

and,   collectively   with  Cornerstone  I,  Cornerstone   II   and

Cornerstone  III,  the "Partnerships") was registered  pursuant  to

Post-Effective Amendment No. 5 to the Registration Statement, which

became effective on February 6, 1987.  The managing underwriter for

the Partnerships is DWR.


The  offering for Cornerstone III originally commenced on  May  31,

1984  and  currently continues with 74,400.002 Units  sold  through

March   31,  1998.   Through  March  31,  1998,  an  aggregate   of

235,388.674  Units  of  the  Partnership  have  been  sold  leaving

14,611.326 Units remaining available for sale as of April 1, 1998.



The  aggregate  offering amount registered was $262,496,000,  based

upon  the initial offering price of $1,050 per Unit ($1,000 initial

Net  Asset Value per Unit, plus a $50 per Unit sales charge on  all

but  80  Units sold to the Partnerships' initial trading  managers)

during  the  Initial  Offering periods  of  May  31,  1984  through

November 30, 1984 with respect to Cornerstone I, Cornerstone II and

Cornerstone  III,  and February 6, 1987 through May  6,  1987  with

respect to Cornerstone IV.

                                
After  the  respective  Initial Offering Periods,  Units  in  the

Partnerships were sold at 107.625% of Net Asset Value  per  Unit,

including  a  charge for offering expenses of 2.5% of  Net  Asset

Value  per Unit, and a sales charge of 5% of the sum of  the  Net

Asset Value per Unit and the charge for offering expenses, during

the "Continuing Offering".

<PAGE>

The  aggregate  price of Units sold through March 31,  1998  with

respect to Cornerstone II is $137,116,764.



Effective September 30, 1984, Cornerstone II, Cornerstone III and

Cornerstone IV were closed to new investors; Units have been sold

since then solely in "Exchanges" with existing investors, at 100%

of Net Asset Value per Unit.  DWR has been paying all expenses in

connection with the offering of Units since September  30,  1994,

without reimbursement.





































<PAGE>







Item 6.  Exhibits and Reports on Form 8-K

     A)  Exhibits - None.

     B)  Reports on Form 8-K. - None.













































<PAGE>



                           SIGNATURE



Pursuant  to the requirements of the Securities Exchange  Act  of
1934, the Registrant has duly caused this report to be signed  on
its behalf by the undersigned, thereunto duly authorized.




                               Dean Witter Cornerstone Fund III
                                        (Registrant)

                               By: Demeter Management Corporation
                                       (General Partner)

May 11, 1998                   By:    /s/    Patti   L.    Behnke
                               Patti L. Behnke
                                       Chief Financial Officer




The  General  Partner which signed the above is  the  only  party
authorized  to  act  for the Registrant.  The Registrant  has  no
principal   executive  officer,  principal   financial   officer,
controller, or principal accounting officer and has no  Board  of
Directors.